= Small-parameter asymptotic of a lattice theta sum
{title2=$(\det A)^{1/2}\theta_\Lambda(A)\to\operatorname{covol}(\Lambda)^{-1}$}
If every eigenvalue of a positive definite symmetric matrix $A$ tends to zero, then the <anisotropic theta functional equation> and the <dominated convergence theorem> show that $(\det A)^{1/2}\theta_\Lambda(A)\to\operatorname{covol}(\Lambda)^{-1}$. Indeed all eigenvalues of $A^{-1}$ tend to infinity, the zero term of the dual <Gaussian theta sum> is one, and its remaining terms tend to zero while being dominated by a fixed summable Gaussian. Merely requiring $\det A\to0$ is insufficient.
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